Wave propagation in general anisotropic media
The use of anisotrpic material, especially in the area of optical fibers and integrated optics, has increased significantly in the past few years; consequently, more theoretical research is needed to find the characteristics of the wave propagation in such materials. Most of the previous studies on this subject consi- dered materials with either electric or magnetic anisotropy [3,8], using one or more coordinate systems. The subject of this thesis is to present a profound study of the wave propagation in general-anisotropic and lossless media, that are electrically and magnetically anisotropic making the permittivities and permeabilities hermitian matrices. These media are considered source-free and homogeneous. We adopt the coordinate-free approach, introduced by Chen , as a mathematical means that greatly facilitates the solutions of our problems. This method is based on direct manipulation of vectors, dyadics, and their invariants, eliminating the use of coordinate systems. In chapter one, we derive the various equations that characterize the wave propagation in unbounded general- anisotropic media, such as the dispersion equation, the directions of the field vectors, and the energy and group velocities. In chapter two, we consider semi-bounded media. We determine Booker quartic equation and the transmission and reflection coefficients at the interface of isotropic- general-anisotropic media where the incident wave is traveling in the isotropic medium. The third chapter is a special case of the first two chapters, considering real diagonal permittivity and permeability matrices with two repeated elements. In this case, the medium is called "Biuniaxial". A more detailed study is conducted in this medium due to its importance in the practical applications. We determine the wave vector surfaces, the directions of the field vectors, the energy densities, the wave vectors, the reflection and transmission coefficients, the rotation of the incident plane of polarization upon reflection and Brewster's angles, and the transmittivities and reflectivi- ties. Chapter four is a direct numerical application of the third chapter. The reflectivities and transmittivities are ploted versus the angle of incidence and compared to those at isotropic-isotropic interfaces. Results and concepts that are difficult to be derived from the mathematical expres- sions are obtained graphically. Finally, we shall mention that the notations used throughout the text of this thesis are defined in appendix A §A.1. Moreover, if the reader wishes to follow the deriva- tions of the equations, we recommend that he has a certain degree of knowledge of tensors and vectors analysis; if not, he can read appendix A as a quick reference.
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:wave propagation general anisotropic media anisotrpic material
Date of Publication:01/01/1986